0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.3R4cy6NfJ7 true 0.08/0.31 % Computer : n023.cluster.edu 0.08/0.31 % Model : x86_64 x86_64 0.08/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.31 % Memory : 8042.1875MB 0.08/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.31 % CPULimit : 1440 0.08/0.31 % WCLimit : 180 0.08/0.31 % DateTime : Mon Jul 3 10:41:21 EDT 2023 0.08/0.31 % CPUTime : 0.08/0.31 % Running portfolio for 1440 s 0.08/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.32 % Number of cores: 8 0.12/0.32 % Python version: Python 3.6.8 0.12/0.32 % Running in HO mode 0.12/0.53 % Total configuration time : 828 0.12/0.53 % Estimated wc time : 1656 0.12/0.53 % Estimated cpu time (8 cpus) : 207.0 0.82/0.64 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.82/0.65 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.82/0.65 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.87/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.87/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.87/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.87/0.81 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.87/0.83 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 3.11/1.28 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 7.18/2.10 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 184.44/30.79 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 381.10/58.08 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 400.91/60.61 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 405.06/61.34 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 455.85/67.88 % Solved by lams/15_lifting3.sh. 455.85/67.88 % done 4156 iterations in 9.692s 455.85/67.88 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 455.85/67.88 % SZS output start Refutation 455.85/67.88 thf(mu_type, type, mu: $tType). 455.85/67.88 thf(mvalid_type, type, mvalid: ($i > $o) > $o). 455.85/67.88 thf('#form17_type', type, '#form17': $o). 455.85/67.88 thf(mreflexive_type, type, mreflexive: ($i > $i > $o) > $o). 455.85/67.88 thf('#sk5_type', type, '#sk5': $i). 455.85/67.88 thf('#form8_type', type, '#form8': $i > $o). 455.85/67.88 thf(mexists_ind_type, type, mexists_ind: (mu > $i > $o) > $i > $o). 455.85/67.88 thf('#sk9_type', type, '#sk9': $i > mu). 455.85/67.88 thf(big_p_type, type, big_p: mu > $i > $o). 455.85/67.88 thf('#form19_type', type, '#form19': mu > $i > $o). 455.85/67.88 thf('#sk2_type', type, '#sk2': $i). 455.85/67.88 thf('#sk20_type', type, '#sk20': $i > mu). 455.85/67.88 thf(rel_s4_type, type, rel_s4: $i > $i > $o). 455.85/67.88 thf('#form3_type', type, '#form3': $o). 455.85/67.88 thf('#form10_type', type, '#form10': $i > $o). 455.85/67.88 thf('#sk13_type', type, '#sk13': $i). 455.85/67.88 thf('#sk6_type', type, '#sk6': $i). 455.85/67.88 thf('#sk7_type', type, '#sk7': mu). 455.85/67.88 thf('#sk11_type', type, '#sk11': $i > $i). 455.85/67.88 thf(mnot_type, type, mnot: ($i > $o) > $i > $o). 455.85/67.88 thf(mor_type, type, mor: ($i > $o) > ($i > $o) > $i > $o). 455.85/67.88 thf('#form12_type', type, '#form12': $o). 455.85/67.88 thf(mtransitive_type, type, mtransitive: ($i > $i > $o) > $o). 455.85/67.88 thf('#sk15_type', type, '#sk15': $i). 455.85/67.88 thf(mimplies_type, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 455.85/67.88 thf('#sk16_type', type, '#sk16': $i > mu). 455.85/67.88 thf('#sk18_type', type, '#sk18': $i). 455.85/67.88 thf(mbox_s4_type, type, mbox_s4: ($i > $o) > $i > $o). 455.85/67.88 thf(exists_in_world_type, type, exists_in_world: mu > $i > $o). 455.85/67.88 thf('#sk1_type', type, '#sk1': $i). 455.85/67.88 thf(mforall_ind_type, type, mforall_ind: (mu > $i > $o) > $i > $o). 455.85/67.88 thf('#sk14_type', type, '#sk14': $i > mu > $i). 455.85/67.88 thf('#sk4_type', type, '#sk4': $i). 455.85/67.88 thf(mand_type, type, mand: ($i > $o) > ($i > $o) > $i > $o). 455.85/67.88 thf(mbox_s4, axiom,(( mbox_s4 ) = 455.85/67.88 (^[Phi:( $i > $o ),W:$i]: 455.85/67.88 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) )))). 455.85/67.88 thf('0', plain, 455.85/67.88 (( mbox_s4 ) = 455.85/67.88 ( ^[Phi:( $i > $o ),W:$i]: 455.85/67.88 ( ![V:$i]: ( ( Phi @ V ) | ( ~( rel_s4 @ W @ V ) ) ) ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mbox_s4])). 455.85/67.88 thf('1', plain, 455.85/67.88 (( mbox_s4 ) = 455.85/67.88 ( ^[V_1:( $i > $o ),V_2:$i]: 455.85/67.88 ( ![X4:$i]: ( ( V_1 @ X4 ) | ( ~( rel_s4 @ V_2 @ X4 ) ) ) ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf(mvalid, axiom,(( mvalid ) = 455.85/67.88 (^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) )))). 455.85/67.88 thf('2', plain, 455.85/67.88 (( mvalid ) = ( ^[Phi:( $i > $o )]: ( ![W:$i]: ( Phi @ W ) ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mvalid])). 455.85/67.88 thf('3', plain, 455.85/67.88 (( mvalid ) = ( ^[V_1:( $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 ) ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf(mexists_ind, axiom,(( mexists_ind ) = 455.85/67.88 (^[Phi:( mu > $i > $o )]: 455.85/67.88 ( mnot @ ( mforall_ind @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) )))). 455.85/67.88 thf(mforall_ind, axiom,(( mforall_ind ) = 455.85/67.88 (^[Phi:( mu > $i > $o ),W:$i]: 455.85/67.88 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) )))). 455.85/67.88 thf('4', plain, 455.85/67.88 (( mforall_ind ) = 455.85/67.88 ( ^[Phi:( mu > $i > $o ),W:$i]: 455.85/67.88 ( ![X:mu]: ( ( exists_in_world @ X @ W ) => ( Phi @ X @ W ) ) ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mforall_ind])). 455.85/67.88 thf('5', plain, 455.85/67.88 (( mforall_ind ) = 455.85/67.88 ( ^[V_1:( mu > $i > $o ),V_2:$i]: 455.85/67.88 ( ![X4:mu]: ( ( exists_in_world @ X4 @ V_2 ) => ( V_1 @ X4 @ V_2 ) ) ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf(mnot, axiom,(( mnot ) = (^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) )))). 455.85/67.88 thf('6', plain, (( mnot ) = ( ^[Phi:( $i > $o ),W:$i]: ( ~( Phi @ W ) ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mnot])). 455.85/67.88 thf('7', plain, 455.85/67.88 (( mnot ) = ( ^[V_1:( $i > $o ),V_2:$i]: ( ~( V_1 @ V_2 ) ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf('8', plain, 455.85/67.88 (( mexists_ind ) = 455.85/67.88 ( ^[Phi:( mu > $i > $o )]: 455.85/67.88 ( mnot @ ( mforall_ind @ ( ^[X:mu]: ( mnot @ ( Phi @ X ) ) ) ) ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mexists_ind, '5', '7'])). 455.85/67.88 thf('9', plain, 455.85/67.88 (( mexists_ind ) = 455.85/67.88 ( ^[V_1:( mu > $i > $o )]: 455.85/67.88 ( mnot @ ( mforall_ind @ ( ^[V_2:mu]: ( mnot @ ( V_1 @ V_2 ) ) ) ) ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf(mimplies, axiom,(( mimplies ) = 455.85/67.88 (^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi )))). 455.85/67.88 thf(mor, axiom,(( mor ) = 455.85/67.88 (^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) )))). 455.85/67.88 thf('10', plain, 455.85/67.88 (( mor ) = 455.85/67.88 ( ^[Phi:( $i > $o ),Psi:( $i > $o ),W:$i]: ( ( Phi @ W ) | ( Psi @ W ) ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mor])). 455.85/67.88 thf('11', plain, 455.85/67.88 (( mor ) = 455.85/67.88 ( ^[V_1:( $i > $o ),V_2:( $i > $o ),V_3:$i]: 455.85/67.88 ( ( V_1 @ V_3 ) | ( V_2 @ V_3 ) ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf('12', plain, 455.85/67.88 (( mimplies ) = 455.85/67.88 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: ( mor @ ( mnot @ Phi ) @ Psi ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mimplies, '11', '7'])). 455.85/67.88 thf('13', plain, 455.85/67.88 (( mimplies ) = 455.85/67.88 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: ( mor @ ( mnot @ V_1 ) @ V_2 ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf(mand, axiom,(( mand ) = 455.85/67.88 (^[Phi:( $i > $o ),Psi:( $i > $o )]: 455.85/67.88 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) )))). 455.85/67.88 thf('14', plain, 455.85/67.88 (( mand ) = 455.85/67.88 ( ^[Phi:( $i > $o ),Psi:( $i > $o )]: 455.85/67.88 ( mnot @ ( mor @ ( mnot @ Phi ) @ ( mnot @ Psi ) ) ) )), 455.85/67.88 inference('simplify_rw_rule', [status(thm)], [mand, '11', '7'])). 455.85/67.88 thf('15', plain, 455.85/67.88 (( mand ) = 455.85/67.88 ( ^[V_1:( $i > $o ),V_2:( $i > $o )]: 455.85/67.88 ( mnot @ ( mor @ ( mnot @ V_1 ) @ ( mnot @ V_2 ) ) ) )), 455.85/67.88 define([status(thm)])). 455.85/67.88 thf(x2128, conjecture, 455.85/67.88 (mvalid @ 455.85/67.88 ( mand @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ 455.85/67.88 ( ^[X:mu]: 455.85/67.88 ( mand @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mbox_s4 @ ( big_p @ X ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ 455.85/67.88 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ 455.85/67.88 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) @ 455.85/67.88 ( mand @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 455.85/67.88 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mand @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 455.85/67.88 ( mexists_ind @ ( ^[X:mu]: ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ 455.85/67.88 ( ^[X:mu]: 455.85/67.88 ( mand @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mbox_s4 @ ( big_p @ X ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ 455.85/67.88 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mimplies @ 455.85/67.88 ( mbox_s4 @ 455.85/67.88 ( mforall_ind @ 455.85/67.88 ( ^[Y:mu]: ( mbox_s4 @ ( big_p @ Y ) ) ) ) ) @ 455.85/67.88 ( mbox_s4 @ ( big_p @ X ) ) ) ) ) ) ) ) ) ) ))). 455.85/67.88 thf(zf_stmt_0, conjecture, 455.85/67.88 (![X4:$i]: 455.85/67.88 ( ~( ( ~( ![X56:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X4 @ X56 ) ) | 455.85/67.88 ( ![X82:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X56 @ X82 ) ) | 455.85/67.88 ( ![X84:mu]: 455.85/67.88 ( ( exists_in_world @ X84 @ X82 ) => 455.85/67.88 ( ~( ( ~( ![X96:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X82 @ X96 ) ) | 455.85/67.88 ( ![X104:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X96 @ X104 ) ) | 455.85/67.88 ( big_p @ X84 @ X104 ) ) ) | 455.85/67.88 ( ~( ![X98:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X96 @ X98 ) ) | 455.85/67.88 ( ![X100:mu]: 455.85/67.88 ( ( exists_in_world @ X100 @ X98 ) => 455.85/67.88 ( ![X102:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X98 @ X102 ) ) | 455.85/67.88 ( big_p @ X100 @ X102 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X86:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X82 @ X86 ) ) | 455.85/67.88 ( ![X90:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X86 @ X90 ) ) | 455.85/67.88 ( ![X92:mu]: 455.85/67.88 ( ( exists_in_world @ X92 @ X90 ) => 455.85/67.88 ( ![X94:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X90 @ X94 ) ) | 455.85/67.88 ( big_p @ X92 @ X94 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X88:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X86 @ X88 ) ) | 455.85/67.88 ( big_p @ X84 @ X88 ) ) ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X58:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X56 @ X58 ) ) | 455.85/67.88 ( ![X64:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X58 @ X64 ) ) | 455.85/67.88 ( ![X66:mu]: 455.85/67.88 ( ( exists_in_world @ X66 @ X64 ) => 455.85/67.88 ( ![X68:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X64 @ X68 ) ) | 455.85/67.88 ( big_p @ X66 @ X68 ) ) ) ) ) ) ) | 455.85/67.88 ( ![X60:mu]: 455.85/67.88 ( ( exists_in_world @ X60 @ X58 ) => 455.85/67.88 ( ~( ![X62:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X58 @ X62 ) ) | 455.85/67.88 ( big_p @ X60 @ X62 ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X70:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X56 @ X70 ) ) | 455.85/67.88 ( ~( ![X78:mu]: 455.85/67.88 ( ( exists_in_world @ X78 @ X70 ) => 455.85/67.88 ( ~( ![X80:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X70 @ X80 ) ) | 455.85/67.88 ( big_p @ X78 @ X80 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X72:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X70 @ X72 ) ) | 455.85/67.88 ( ![X74:mu]: 455.85/67.88 ( ( exists_in_world @ X74 @ X72 ) => 455.85/67.88 ( ![X76:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X72 @ X76 ) ) | 455.85/67.88 ( big_p @ X74 @ X76 ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X6:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 455.85/67.88 ( ~( ( ~( ![X44:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X6 @ X44 ) ) | 455.85/67.88 ( ~( ![X52:mu]: 455.85/67.88 ( ( exists_in_world @ X52 @ X44 ) => 455.85/67.88 ( ~( ![X54:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X44 @ X54 ) ) | 455.85/67.88 ( big_p @ X52 @ X54 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X46:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X44 @ X46 ) ) | 455.85/67.88 ( ![X48:mu]: 455.85/67.88 ( ( exists_in_world @ X48 @ X46 ) => 455.85/67.88 ( ![X50:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X46 @ X50 ) ) | 455.85/67.88 ( big_p @ X48 @ X50 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X32:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X6 @ X32 ) ) | 455.85/67.88 ( ![X38:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X32 @ X38 ) ) | 455.85/67.88 ( ![X40:mu]: 455.85/67.88 ( ( exists_in_world @ X40 @ X38 ) => 455.85/67.88 ( ![X42:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X38 @ X42 ) ) | 455.85/67.88 ( big_p @ X40 @ X42 ) ) ) ) ) ) ) | 455.85/67.88 ( ![X34:mu]: 455.85/67.88 ( ( exists_in_world @ X34 @ X32 ) => 455.85/67.88 ( ~( ![X36:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X32 @ X36 ) ) | 455.85/67.88 ( big_p @ X34 @ X36 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X8:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X6 @ X8 ) ) | 455.85/67.88 ( ![X10:mu]: 455.85/67.88 ( ( exists_in_world @ X10 @ X8 ) => 455.85/67.88 ( ~( ( ~( ![X22:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X8 @ X22 ) ) | 455.85/67.88 ( ![X30:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X22 @ X30 ) ) | 455.85/67.88 ( big_p @ X10 @ X30 ) ) ) | 455.85/67.88 ( ~( ![X24:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X22 @ X24 ) ) | 455.85/67.88 ( ![X26:mu]: 455.85/67.88 ( ( exists_in_world @ 455.85/67.88 X26 @ X24 ) => 455.85/67.88 ( ![X28:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X24 @ X28 ) ) | 455.85/67.88 ( big_p @ X26 @ X28 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X12:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X8 @ X12 ) ) | 455.85/67.88 ( ![X16:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X12 @ X16 ) ) | 455.85/67.88 ( ![X18:mu]: 455.85/67.88 ( ( exists_in_world @ X18 @ X16 ) => 455.85/67.88 ( ![X20:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X16 @ X20 ) ) | 455.85/67.88 ( big_p @ X18 @ X20 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X14:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X12 @ X14 ) ) | 455.85/67.88 ( big_p @ X10 @ X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 455.85/67.88 thf(zf_stmt_1, negated_conjecture, 455.85/67.88 (~( ![X4:$i]: 455.85/67.88 ( ~( ( ~( ![X56:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X4 @ X56 ) ) | 455.85/67.88 ( ![X82:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X56 @ X82 ) ) | 455.85/67.88 ( ![X84:mu]: 455.85/67.88 ( ( exists_in_world @ X84 @ X82 ) => 455.85/67.88 ( ~( ( ~( ![X96:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X82 @ X96 ) ) | 455.85/67.88 ( ![X104:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X96 @ X104 ) ) | 455.85/67.88 ( big_p @ X84 @ X104 ) ) ) | 455.85/67.88 ( ~( ![X98:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X96 @ X98 ) ) | 455.85/67.88 ( ![X100:mu]: 455.85/67.88 ( ( exists_in_world @ 455.85/67.88 X100 @ X98 ) => 455.85/67.88 ( ![X102:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X98 @ X102 ) ) | 455.85/67.88 ( big_p @ X100 @ X102 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X86:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X82 @ X86 ) ) | 455.85/67.88 ( ![X90:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X86 @ X90 ) ) | 455.85/67.88 ( ![X92:mu]: 455.85/67.88 ( ( exists_in_world @ X92 @ X90 ) => 455.85/67.88 ( ![X94:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X90 @ X94 ) ) | 455.85/67.88 ( big_p @ X92 @ X94 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X88:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X86 @ X88 ) ) | 455.85/67.88 ( big_p @ X84 @ X88 ) ) ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X58:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X56 @ X58 ) ) | 455.85/67.88 ( ![X64:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X58 @ X64 ) ) | 455.85/67.88 ( ![X66:mu]: 455.85/67.88 ( ( exists_in_world @ X66 @ X64 ) => 455.85/67.88 ( ![X68:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X64 @ X68 ) ) | 455.85/67.88 ( big_p @ X66 @ X68 ) ) ) ) ) ) ) | 455.85/67.88 ( ![X60:mu]: 455.85/67.88 ( ( exists_in_world @ X60 @ X58 ) => 455.85/67.88 ( ~( ![X62:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X58 @ X62 ) ) | 455.85/67.88 ( big_p @ X60 @ X62 ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X70:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X56 @ X70 ) ) | 455.85/67.88 ( ~( ![X78:mu]: 455.85/67.88 ( ( exists_in_world @ X78 @ X70 ) => 455.85/67.88 ( ~( ![X80:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X70 @ X80 ) ) | 455.85/67.88 ( big_p @ X78 @ X80 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X72:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X70 @ X72 ) ) | 455.85/67.88 ( ![X74:mu]: 455.85/67.88 ( ( exists_in_world @ X74 @ X72 ) => 455.85/67.88 ( ![X76:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X72 @ X76 ) ) | 455.85/67.88 ( big_p @ X74 @ X76 ) ) ) ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X6:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X4 @ X6 ) ) | 455.85/67.88 ( ~( ( ~( ![X44:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X6 @ X44 ) ) | 455.85/67.88 ( ~( ![X52:mu]: 455.85/67.88 ( ( exists_in_world @ X52 @ X44 ) => 455.85/67.88 ( ~( ![X54:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X44 @ X54 ) ) | 455.85/67.88 ( big_p @ X52 @ X54 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X46:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X44 @ X46 ) ) | 455.85/67.88 ( ![X48:mu]: 455.85/67.88 ( ( exists_in_world @ X48 @ X46 ) => 455.85/67.88 ( ![X50:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X46 @ X50 ) ) | 455.85/67.88 ( big_p @ X48 @ X50 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X32:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X6 @ X32 ) ) | 455.85/67.88 ( ![X38:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X32 @ X38 ) ) | 455.85/67.88 ( ![X40:mu]: 455.85/67.88 ( ( exists_in_world @ X40 @ X38 ) => 455.85/67.88 ( ![X42:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X38 @ X42 ) ) | 455.85/67.88 ( big_p @ X40 @ X42 ) ) ) ) ) ) ) | 455.85/67.88 ( ![X34:mu]: 455.85/67.88 ( ( exists_in_world @ X34 @ X32 ) => 455.85/67.88 ( ~( ![X36:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X32 @ X36 ) ) | 455.85/67.88 ( big_p @ X34 @ X36 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X8:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X6 @ X8 ) ) | 455.85/67.88 ( ![X10:mu]: 455.85/67.88 ( ( exists_in_world @ X10 @ X8 ) => 455.85/67.88 ( ~( ( ~( ![X22:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X8 @ X22 ) ) | 455.85/67.88 ( ![X30:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X22 @ X30 ) ) | 455.85/67.88 ( big_p @ X10 @ X30 ) ) ) | 455.85/67.88 ( ~( ![X24:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X22 @ X24 ) ) | 455.85/67.88 ( ![X26:mu]: 455.85/67.88 ( ( exists_in_world @ 455.85/67.88 X26 @ X24 ) => 455.85/67.88 ( ![X28:$i]: 455.85/67.88 ( ( ~( rel_s4 @ 455.85/67.88 X24 @ X28 ) ) | 455.85/67.88 ( big_p @ X26 @ X28 ) ) ) ) ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X12:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X8 @ X12 ) ) | 455.85/67.88 ( ![X16:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X12 @ X16 ) ) | 455.85/67.88 ( ![X18:mu]: 455.85/67.88 ( ( exists_in_world @ 455.85/67.88 X18 @ X16 ) => 455.85/67.88 ( ![X20:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X16 @ X20 ) ) | 455.85/67.88 ( big_p @ X18 @ X20 ) ) ) ) ) ) ) | 455.85/67.88 ( ~( ![X14:$i]: 455.85/67.88 ( ( ~( rel_s4 @ X12 @ X14 ) ) | 455.85/67.88 ( big_p @ X10 @ X14 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 455.85/67.88 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 455.85/67.88 thf(zip_derived_cl4, plain, 455.85/67.88 (~ (((!!) @ (^[Y0 : $i]: 455.85/67.88 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.88 (((!!) @ (^[Y2 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y5)))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y6 @ 455.85/67.88 Y5) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y7 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y5 @ Y7))) | 455.85/67.88 (big_p @ 455.85/67.88 Y6 @ Y7))))))))))))))))))))))))) | 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y6 @ 455.85/67.88 Y5) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y7 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y5 @ Y7))) | 455.85/67.88 (big_p @ 455.85/67.88 Y6 @ Y7)))))))))))))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y5))))))))))))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y3))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y4 @ 455.85/67.88 Y3) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y4 @ Y5)))))))))))))))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4)))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4))))))))))))))) | 455.85/67.88 (((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y3))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y4 @ 455.85/67.88 Y3) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y4 @ Y5)))))))))))))))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.88 (((~) @ (((((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 ((( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4))))))))))))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y3))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y4 @ 455.85/67.88 Y3) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y4 @ Y5))))))))))))))))))))))))) | 455.85/67.88 (((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 ((( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y3))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y4 @ 455.85/67.88 Y3) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y4 @ Y5)))))))))))))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4)))))))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y5)))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y6 @ 455.85/67.88 Y5) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y7 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y5 @ Y7))) | 455.85/67.88 (big_p @ 455.85/67.88 Y6 @ Y7))))))))))))))))))))))))) | 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y6 @ 455.85/67.88 Y5) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y7 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y5 @ Y7))) | 455.85/67.88 (big_p @ 455.85/67.88 Y6 @ Y7)))))))))))))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y5))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y5)))))))))))))))))))))))))))))))))))))))))))))), 455.85/67.88 inference('cnf', [status(esa)], [zf_stmt_1])). 455.85/67.88 thf(zip_derived_cl5, plain, 455.85/67.88 ( (((((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.88 (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.88 (((!!) @ (^[Y2 : mu]: 455.85/67.88 (((exists_in_world @ 455.85/67.88 Y2 @ Y1) => 455.85/67.88 (((~) @ (((( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y4)))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y5 @ 455.85/67.88 Y4) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y6))) | 455.85/67.88 (big_p @ 455.85/67.88 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y5 @ 455.85/67.88 Y4) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y6))) | 455.85/67.88 (big_p @ 455.85/67.88 Y5 @ Y6)))))))))))))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y4))))))))))))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.88 (((!!) @ (^[Y2 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4)))))))))))))))) | 455.85/67.88 (((!!) @ (^[Y2 : mu]: 455.85/67.88 (((exists_in_world @ 455.85/67.88 Y2 @ Y1) => 455.85/67.88 (((~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y3)))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.88 (((~) @ (((!!) @ ( 455.85/67.88 ^[Y2 : mu]: 455.85/67.88 (((exists_in_world @ 455.85/67.88 Y2 @ Y1) => 455.85/67.88 (((~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y3))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4)))))))))))))))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.88 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y0 @ Y1))) | 455.85/67.88 (((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y2 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y2 @ 455.85/67.88 Y1) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y3))))))))))))))) | 455.85/67.88 (((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y0 @ Y1))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y2 : $i]: 455.85/67.88 (((( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y2))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y3 @ 455.85/67.88 Y2) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y2 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y3 @ Y4)))))))))))))))) | 455.85/67.88 (((!!) @ ( 455.85/67.88 ^[Y2 : mu]: 455.85/67.88 (((exists_in_world @ 455.85/67.88 Y2 @ 455.85/67.88 Y1) => 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.88 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.88 (((!!) @ (^[Y2 : mu]: 455.85/67.88 (((exists_in_world @ 455.85/67.88 Y2 @ Y1) => 455.85/67.88 (((~) @ ( 455.85/67.88 ( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y4)))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y5 @ 455.85/67.88 Y4) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y6))) | 455.85/67.88 (big_p @ 455.85/67.88 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (( 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y5 @ 455.85/67.88 Y4) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y6))) | 455.85/67.88 (big_p @ 455.85/67.88 Y5 @ Y6)))))))))))))))) | 455.85/67.88 ( 455.85/67.88 ( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y4))))))))))))))))))))))))))))))))))))))))), 455.85/67.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl4])). 455.85/67.88 thf(zip_derived_cl6, plain, 455.85/67.88 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.88 (((!!) @ (^[Y1 : $i]: 455.85/67.88 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.88 (((!!) @ (^[Y2 : mu]: 455.85/67.88 (((exists_in_world @ Y2 @ 455.85/67.88 Y1) => 455.85/67.88 (((~) @ (((((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (((( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (big_p @ 455.85/67.88 Y2 @ Y4)))))) | 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 ( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y5 @ 455.85/67.88 Y4) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y6))) | 455.85/67.88 (big_p @ 455.85/67.88 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.88 (((~) @ ( 455.85/67.88 ((!!) @ ( 455.85/67.88 ^[Y3 : $i]: 455.85/67.88 (((( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y1 @ Y3))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y4 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y3 @ Y4))) | 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y5 : mu]: 455.85/67.88 (( 455.85/67.88 (exists_in_world @ 455.85/67.88 Y5 @ 455.85/67.88 Y4) => 455.85/67.88 (( 455.85/67.88 (!!) @ ( 455.85/67.88 ^[Y6 : $i]: 455.85/67.88 (( 455.85/67.88 (( 455.85/67.88 (~) @ ( 455.85/67.88 rel_s4 @ 455.85/67.88 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4))))))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (((!!) @ (^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl5])). 455.85/67.89 thf(zip_derived_cl7, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk1' @ '#sk2'))) | 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3))))))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2)))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 455.85/67.89 thf(zip_derived_cl9, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 ((( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 ((( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3))))))))))))))))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 455.85/67.89 thf(zip_derived_cl8, plain, 455.85/67.89 (( (rel_s4 @ '#sk1' @ '#sk2') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 455.85/67.89 thf(zip_derived_cl12, plain, 455.85/67.89 (( ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl15, plain, 455.85/67.89 ((~ ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3))))))))))))))))))))))))))))))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl9, zip_derived_cl12])). 455.85/67.89 thf(zip_derived_cl21, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk2' @ '#sk5'))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ '#sk5') => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 '#sk5' @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 '#sk5' @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))))))))))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl15])). 455.85/67.89 thf(zip_derived_cl27, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ '#sk5') => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 '#sk5' @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 '#sk5' @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))))))))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 455.85/67.89 thf(zip_derived_cl32, plain, 455.85/67.89 ((~ (((exists_in_world @ '#sk7' @ '#sk5') => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1)))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (big_p @ 455.85/67.89 '#sk7' @ Y1))))))))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])). 455.85/67.89 thf(zip_derived_cl44, plain, 455.85/67.89 (( (((((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1)))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])). 455.85/67.89 thf(zip_derived_cl60, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | (big_p @ 455.85/67.89 '#sk7' @ Y1)))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 455.85/67.89 thf(zip_derived_cl74, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk15'))) | 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | (big_p @ 455.85/67.89 '#sk7' @ Y0)))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 455.85/67.89 thf(zip_derived_cl85, plain, 455.85/67.89 (( (rel_s4 @ '#sk5' @ '#sk15') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 455.85/67.89 thf(zip_derived_cl98, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl99, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk5' @ '#sk18'))) | 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | (big_p @ 455.85/67.89 '#sk7' @ Y0)))))))))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 455.85/67.89 thf(zip_derived_cl111, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 455.85/67.89 thf(zip_derived_cl126, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk18')) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 ('#sk11' @ '#sk18') @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 455.85/67.89 thf(zip_derived_cl135, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk18')) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ 455.85/67.89 Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 455.85/67.89 thf(zip_derived_cl139, plain, 455.85/67.89 ((~ (((exists_in_world @ ('#sk16' @ '#sk18') @ ('#sk11' @ '#sk18')) => 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ Y0))) | 455.85/67.89 (big_p @ ('#sk16' @ '#sk18') @ Y0)))))))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl135])). 455.85/67.89 thf(zip_derived_cl141, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ Y0))) | 455.85/67.89 (big_p @ ('#sk16' @ '#sk18') @ Y0)))))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 455.85/67.89 thf(zip_derived_cl142, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ ('#sk11' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))))) | 455.85/67.89 (big_p @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl141])). 455.85/67.89 thf(zip_derived_cl143, plain, 455.85/67.89 (( (rel_s4 @ ('#sk11' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 455.85/67.89 thf(zip_derived_cl140, plain, 455.85/67.89 (( (exists_in_world @ ('#sk16' @ '#sk18') @ ('#sk11' @ '#sk18')) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl139])). 455.85/67.89 thf(cumulative_ax, axiom, 455.85/67.89 (![X:mu,V:$i,W:$i]: 455.85/67.89 ( ( ( exists_in_world @ X @ V ) & ( rel_s4 @ V @ W ) ) => 455.85/67.89 ( exists_in_world @ X @ W ) ))). 455.85/67.89 thf(zip_derived_cl3, plain, 455.85/67.89 ( (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((exists_in_world @ Y0 @ Y1) & 455.85/67.89 (rel_s4 @ Y1 @ Y2))) => 455.85/67.89 (exists_in_world @ Y0 @ Y2))))))))))))), 455.85/67.89 inference('cnf', [status(esa)], [cumulative_ax])). 455.85/67.89 thf(zip_derived_cl191, plain, 455.85/67.89 (![X2 : mu]: 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((exists_in_world @ X2 @ Y0) & (rel_s4 @ 455.85/67.89 Y0 @ Y1))) => 455.85/67.89 (exists_in_world @ X2 @ Y1)))))))))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 455.85/67.89 thf(zip_derived_cl192, plain, 455.85/67.89 (![X2 : mu, X4 : $i]: 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ Y0))) => 455.85/67.89 (exists_in_world @ X2 @ Y0))))))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl191])). 455.85/67.89 thf(zip_derived_cl193, plain, 455.85/67.89 (![X2 : mu, X4 : $i, X6 : $i]: 455.85/67.89 (((((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) => 455.85/67.89 (exists_in_world @ X2 @ X6)))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl192])). 455.85/67.89 thf(zip_derived_cl194, plain, 455.85/67.89 (![X2 : mu, X4 : $i, X6 : $i]: 455.85/67.89 (~ (((exists_in_world @ X2 @ X4) & (rel_s4 @ X4 @ X6))) 455.85/67.89 | (exists_in_world @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl193])). 455.85/67.89 thf(zip_derived_cl195, plain, 455.85/67.89 (![X2 : mu, X4 : $i, X6 : $i]: 455.85/67.89 (~ (exists_in_world @ X2 @ X4) 455.85/67.89 | ~ (rel_s4 @ X4 @ X6) 455.85/67.89 | (exists_in_world @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 455.85/67.89 thf(zip_derived_cl744, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( ('#form17') 455.85/67.89 | (exists_in_world @ ('#sk16' @ '#sk18') @ X0) 455.85/67.89 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl140, zip_derived_cl195])). 455.85/67.89 thf(zip_derived_cl2414, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | (exists_in_world @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl744])). 455.85/67.89 thf(zip_derived_cl2415, plain, 455.85/67.89 (( (exists_in_world @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl2414])). 455.85/67.89 thf(zip_derived_cl134, plain, 455.85/67.89 (( (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')) | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 455.85/67.89 thf(zip_derived_cl143, plain, 455.85/67.89 (( (rel_s4 @ ('#sk11' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 455.85/67.89 thf(mtransitive, axiom,(( mtransitive ) = 455.85/67.89 (^[R:( $i > $i > $o )]: 455.85/67.89 ( ![S:$i,T:$i,U:$i]: 455.85/67.89 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) )))). 455.85/67.89 thf('16', plain, 455.85/67.89 (( mtransitive ) = 455.85/67.89 ( ^[R:( $i > $i > $o )]: 455.85/67.89 ( ![S:$i,T:$i,U:$i]: 455.85/67.89 ( ( ( R @ S @ T ) & ( R @ T @ U ) ) => ( R @ S @ U ) ) ) )), 455.85/67.89 inference('simplify_rw_rule', [status(thm)], [mtransitive])). 455.85/67.89 thf('17', plain, 455.85/67.89 (( mtransitive ) = 455.85/67.89 ( ^[V_1:( $i > $i > $o )]: 455.85/67.89 ( ![X4:$i,X6:$i,X8:$i]: 455.85/67.89 ( ( ( V_1 @ X4 @ X6 ) & ( V_1 @ X6 @ X8 ) ) => ( V_1 @ X4 @ X8 ) ) ) )), 455.85/67.89 define([status(thm)])).thf(a2, axiom, (mtransitive @ rel_s4)). 455.85/67.89 thf(zf_stmt_2, axiom, 455.85/67.89 (![X4:$i,X6:$i,X8:$i]: 455.85/67.89 ( ( ( rel_s4 @ X6 @ X8 ) & ( rel_s4 @ X4 @ X6 ) ) => ( rel_s4 @ X4 @ X8 ) ))). 455.85/67.89 thf(zip_derived_cl1, plain, 455.85/67.89 ( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((rel_s4 @ Y1 @ Y2) & (rel_s4 @ 455.85/67.89 Y0 @ Y1))) => 455.85/67.89 (rel_s4 @ Y0 @ Y2))))))))))))), 455.85/67.89 inference('cnf', [status(esa)], [zf_stmt_2])). 455.85/67.89 thf(zip_derived_cl157, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((rel_s4 @ Y0 @ Y1) & (rel_s4 @ X2 @ Y0))) => 455.85/67.89 (rel_s4 @ X2 @ Y1)))))))))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 455.85/67.89 thf(zip_derived_cl158, plain, 455.85/67.89 (![X2 : $i, X4 : $i]: 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((rel_s4 @ X4 @ Y0) & (rel_s4 @ X2 @ X4))) => 455.85/67.89 (rel_s4 @ X2 @ Y0))))))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl157])). 455.85/67.89 thf(zip_derived_cl159, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : $i]: 455.85/67.89 (((((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) => (rel_s4 @ X2 @ X6)))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl158])). 455.85/67.89 thf(zip_derived_cl160, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : $i]: 455.85/67.89 (~ (((rel_s4 @ X4 @ X6) & (rel_s4 @ X2 @ X4))) | (rel_s4 @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 455.85/67.89 thf(zip_derived_cl161, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 455.85/67.89 thf(zip_derived_cl776, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( ('#form17') 455.85/67.89 | (rel_s4 @ X0 @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ~ (rel_s4 @ X0 @ ('#sk11' @ '#sk18')))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl143, zip_derived_cl161])). 455.85/67.89 thf(zip_derived_cl7635, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | (rel_s4 @ '#sk18' @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl776])). 455.85/67.89 thf(zip_derived_cl7639, plain, 455.85/67.89 (( (rel_s4 @ '#sk18' @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl7635])). 455.85/67.89 thf(mreflexive, axiom,(( mreflexive ) = 455.85/67.89 (^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) )))). 455.85/67.89 thf('18', plain, 455.85/67.89 (( mreflexive ) = ( ^[R:( $i > $i > $o )]: ( ![S:$i]: ( R @ S @ S ) ) )), 455.85/67.89 inference('simplify_rw_rule', [status(thm)], [mreflexive])). 455.85/67.89 thf('19', plain, 455.85/67.89 (( mreflexive ) = 455.85/67.89 ( ^[V_1:( $i > $i > $o )]: ( ![X4:$i]: ( V_1 @ X4 @ X4 ) ) )), 455.85/67.89 define([status(thm)])).thf(a1, axiom, (mreflexive @ rel_s4)). 455.85/67.89 thf(zf_stmt_3, axiom, (![X4:$i]: ( rel_s4 @ X4 @ X4 ))). 455.85/67.89 thf(zip_derived_cl2, plain, ( (((!!) @ (^[Y0 : $i]: (rel_s4 @ Y0 @ Y0))))), 455.85/67.89 inference('cnf', [status(esa)], [zf_stmt_3])). 455.85/67.89 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 455.85/67.89 thf(zip_derived_cl12, plain, 455.85/67.89 (( ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl13, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk1' @ '#sk4'))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y1 @ Y0) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3))))))))))))))))))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 455.85/67.89 thf(zip_derived_cl19, plain, 455.85/67.89 (( (((((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ 455.85/67.89 Y0) => 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2)))))))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])). 455.85/67.89 thf(zip_derived_cl24, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl19])). 455.85/67.89 thf(zip_derived_cl30, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk4' @ '#sk6'))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ '#sk6') => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 '#sk6' @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 455.85/67.89 thf(zip_derived_cl41, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 455.85/67.89 thf(zip_derived_cl56, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form10' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl57, plain, 455.85/67.89 (![X2 : $i, X4 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ X2 @ X4))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X4) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ~ ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl56])). 455.85/67.89 thf(zip_derived_cl71, plain, 455.85/67.89 (![X2 : $i, X4 : $i]: 455.85/67.89 (~ (rel_s4 @ X2 @ X4) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X4) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))) 455.85/67.89 | ~ ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl57])). 455.85/67.89 thf(zip_derived_cl82, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu]: 455.85/67.89 ( (((exists_in_world @ X6 @ X4) => 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))))) 455.85/67.89 | ~ ('#form10' @ X2) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 455.85/67.89 thf(zip_derived_cl95, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu]: 455.85/67.89 (~ (exists_in_world @ X6 @ X4) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4) 455.85/67.89 | ~ ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 455.85/67.89 thf(zip_derived_cl107, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ X4 @ X8))) | (big_p @ X6 @ X8))) 455.85/67.89 | ~ ('#form10' @ X2) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4) 455.85/67.89 | ~ (exists_in_world @ X6 @ X4))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 455.85/67.89 thf(zip_derived_cl121, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X8) 455.85/67.89 | (big_p @ X6 @ X8) 455.85/67.89 | ~ (exists_in_world @ X6 @ X4) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4) 455.85/67.89 | ~ ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl107])). 455.85/67.89 thf(zip_derived_cl146, plain, 455.85/67.89 (![X0 : $i, X1 : $i, X2 : mu]: 455.85/67.89 (~ ('#form10' @ X1) 455.85/67.89 | ~ (rel_s4 @ X1 @ X0) 455.85/67.89 | ~ (exists_in_world @ X2 @ X0) 455.85/67.89 | (big_p @ X2 @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl121])). 455.85/67.89 thf(zip_derived_cl7690, plain, 455.85/67.89 (![X0 : mu]: 455.85/67.89 ( ('#form17') 455.85/67.89 | (big_p @ X0 @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ~ (exists_in_world @ X0 @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ~ ('#form10' @ '#sk18'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl7639, zip_derived_cl146])). 455.85/67.89 thf(zip_derived_cl29455, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | ~ ('#form10' @ '#sk18') 455.85/67.89 | (big_p @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl2415, zip_derived_cl7690])). 455.85/67.89 thf(zip_derived_cl29463, plain, 455.85/67.89 (( (big_p @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ~ ('#form10' @ '#sk18') 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl29455])). 455.85/67.89 thf(zip_derived_cl144, plain, 455.85/67.89 ((~ (big_p @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 455.85/67.89 thf(zip_derived_cl29467, plain, (( ('#form17') | ~ ('#form10' @ '#sk18'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl29463, zip_derived_cl144])). 455.85/67.89 thf(zip_derived_cl85, plain, 455.85/67.89 (( (rel_s4 @ '#sk5' @ '#sk15') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 455.85/67.89 thf(zip_derived_cl98, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl100, plain, 455.85/67.89 ((~ ('#form17') | ~ ('#form3') | (rel_s4 @ '#sk5' @ '#sk15'))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl85, zip_derived_cl98])). 455.85/67.89 thf(zip_derived_cl43, plain, 455.85/67.89 (( (exists_in_world @ '#sk7' @ '#sk5') | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])). 455.85/67.89 thf(zip_derived_cl195, plain, 455.85/67.89 (![X2 : mu, X4 : $i, X6 : $i]: 455.85/67.89 (~ (exists_in_world @ X2 @ X4) 455.85/67.89 | ~ (rel_s4 @ X4 @ X6) 455.85/67.89 | (exists_in_world @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 455.85/67.89 thf(zip_derived_cl207, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 (~ ('#form3') 455.85/67.89 | (exists_in_world @ '#sk7' @ X0) 455.85/67.89 | ~ (rel_s4 @ '#sk5' @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl195])). 455.85/67.89 thf(zip_derived_cl385, plain, 455.85/67.89 ((~ ('#form3') 455.85/67.89 | ~ ('#form17') 455.85/67.89 | (exists_in_world @ '#sk7' @ '#sk15') 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl207])). 455.85/67.89 thf(zip_derived_cl387, plain, 455.85/67.89 (( (exists_in_world @ '#sk7' @ '#sk15') | ~ ('#form17') | ~ ('#form3'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl385])). 455.85/67.89 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 455.85/67.89 thf(zip_derived_cl86, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | (big_p @ '#sk7' @ 455.85/67.89 Y0)))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 455.85/67.89 thf(zip_derived_cl98, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl101, plain, 455.85/67.89 ((~ ('#form17') 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | (big_p @ 455.85/67.89 '#sk7' @ Y0)))))))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl86, zip_derived_cl98])). 455.85/67.89 thf(zip_derived_cl113, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk15' @ ('#sk14' @ '#sk15' @ '#sk7')))) | 455.85/67.89 (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')))) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ ('#form17'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 455.85/67.89 thf(zip_derived_cl128, plain, 455.85/67.89 (( (rel_s4 @ '#sk15' @ ('#sk14' @ '#sk15' @ '#sk7')) 455.85/67.89 | ~ ('#form17') 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])). 455.85/67.89 thf(zip_derived_cl121, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X8) 455.85/67.89 | (big_p @ X6 @ X8) 455.85/67.89 | ~ (exists_in_world @ X6 @ X4) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4) 455.85/67.89 | ~ ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl107])). 455.85/67.89 thf(zip_derived_cl585, plain, 455.85/67.89 (![X0 : $i, X1 : mu]: 455.85/67.89 (~ ('#form3') 455.85/67.89 | ~ ('#form17') 455.85/67.89 | ~ ('#form10' @ X0) 455.85/67.89 | ~ (rel_s4 @ X0 @ '#sk15') 455.85/67.89 | ~ (exists_in_world @ X1 @ '#sk15') 455.85/67.89 | (big_p @ X1 @ ('#sk14' @ '#sk15' @ '#sk7')))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl121])). 455.85/67.89 thf(zip_derived_cl3508, plain, 455.85/67.89 (![X0 : mu]: 455.85/67.89 ( (big_p @ X0 @ ('#sk14' @ '#sk15' @ '#sk7')) 455.85/67.89 | ~ (exists_in_world @ X0 @ '#sk15') 455.85/67.89 | ~ ('#form10' @ '#sk15') 455.85/67.89 | ~ ('#form17') 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl585])). 455.85/67.89 thf(zip_derived_cl87, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk15' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl74])). 455.85/67.89 thf(zip_derived_cl56, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form10' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl11, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 455.85/67.89 thf(zip_derived_cl12, plain, 455.85/67.89 (( ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl17, plain, 455.85/67.89 ((~ ('#form3') 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y2))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl11, zip_derived_cl12])). 455.85/67.89 thf(zip_derived_cl23, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ '#sk2' @ X2))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ 455.85/67.89 Y2)))))))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 455.85/67.89 thf(zip_derived_cl29, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (rel_s4 @ '#sk2' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 455.85/67.89 thf(zip_derived_cl29, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (rel_s4 @ '#sk2' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 455.85/67.89 thf(zip_derived_cl36, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form8' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl10, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ Y2 @ 455.85/67.89 Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])). 455.85/67.89 thf(zip_derived_cl12, plain, 455.85/67.89 (( ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk1' @ Y0))) | 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((~) @ ( 455.85/67.89 ((((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6))))))))))))))))))))))))) | 455.85/67.89 (((~) @ ( 455.85/67.89 ((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y5 @ 455.85/67.89 Y4) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y6 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y4 @ Y6))) | 455.85/67.89 (big_p @ 455.85/67.89 Y5 @ Y6)))))))))))))))) | 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y4)))))))))))))))))))))))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl16, plain, 455.85/67.89 ((~ ('#form3') 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk2' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl10, zip_derived_cl12])). 455.85/67.89 thf(zip_derived_cl22, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ '#sk2' @ X2))) | 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 455.85/67.89 thf(zip_derived_cl28, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (rel_s4 @ '#sk2' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 455.85/67.89 thf(zip_derived_cl33, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form8' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl38, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form8' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl29, zip_derived_cl36, zip_derived_cl33])). 455.85/67.89 thf(zip_derived_cl47, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form10' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl102, plain, 455.85/67.89 (( ('#form10' @ '#sk15') 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl87, zip_derived_cl56, zip_derived_cl47])). 455.85/67.89 thf(zip_derived_cl98, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk5' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ '#sk7' @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl114, plain, 455.85/67.89 ((~ ('#form17') | ~ ('#form3') | ('#form10' @ '#sk15'))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl102, zip_derived_cl98])). 455.85/67.89 thf(zip_derived_cl3515, plain, 455.85/67.89 (![X0 : mu]: 455.85/67.89 (~ ('#form3') 455.85/67.89 | ~ ('#form17') 455.85/67.89 | ~ (exists_in_world @ X0 @ '#sk15') 455.85/67.89 | (big_p @ X0 @ ('#sk14' @ '#sk15' @ '#sk7')))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl3508, zip_derived_cl114])). 455.85/67.89 thf(zip_derived_cl3516, plain, 455.85/67.89 ((~ ('#form3') 455.85/67.89 | ~ ('#form17') 455.85/67.89 | (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')) 455.85/67.89 | ~ ('#form17') 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl387, zip_derived_cl3515])). 455.85/67.89 thf(zip_derived_cl3522, plain, 455.85/67.89 (( (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')) 455.85/67.89 | ~ ('#form17') 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl3516])). 455.85/67.89 thf(zip_derived_cl129, plain, 455.85/67.89 ((~ (big_p @ '#sk7' @ ('#sk14' @ '#sk15' @ '#sk7')) 455.85/67.89 | ~ ('#form17') 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl113])). 455.85/67.89 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 455.85/67.89 thf(zip_derived_cl20, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3)))))) | 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y4 @ 455.85/67.89 Y3) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y5 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y3 @ Y5))) | 455.85/67.89 (big_p @ 455.85/67.89 Y4 @ Y5)))))))))))))))) | 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 ( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y1 @ Y3))))))))))))))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl13])). 455.85/67.89 thf(zip_derived_cl25, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ '#sk4' @ X2))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 X2 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 X2 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))))))))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 455.85/67.89 thf(zip_derived_cl31, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 X2 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 X2 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y3 @ 455.85/67.89 Y2) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y4 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y2 @ Y4))) | 455.85/67.89 (big_p @ 455.85/67.89 Y3 @ Y4)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ ( 455.85/67.89 ^[Y2 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y2))) | 455.85/67.89 (big_p @ 455.85/67.89 Y0 @ Y2)))))))))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl25])). 455.85/67.89 thf(zip_derived_cl42, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 ( (((exists_in_world @ X4 @ X2) => 455.85/67.89 (((~) @ (((((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (big_p @ X4 @ Y1)))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y2 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (big_p @ 455.85/67.89 X4 @ Y1))))))))))))))))))))) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 455.85/67.89 thf(zip_derived_cl59, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 (~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ (((((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ X4 @ Y1)))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (( 455.85/67.89 (exists_in_world @ 455.85/67.89 Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (( 455.85/67.89 (!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 (( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3))))))))))))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ 455.85/67.89 Y2 @ Y1) => 455.85/67.89 (((!!) @ ( 455.85/67.89 ^[Y3 : $i]: 455.85/67.89 ( 455.85/67.89 ( 455.85/67.89 (( 455.85/67.89 (~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 Y0 @ Y1))) | 455.85/67.89 (big_p @ X4 @ Y1))))))))))))))))) 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 455.85/67.89 thf(zip_derived_cl73, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 ( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (big_p @ X4 @ Y1))))))))))))) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl59])). 455.85/67.89 thf(zip_derived_cl84, plain, 455.85/67.89 (![X2 : $i, X4 : mu, X6 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ X2 @ X6))) | 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) | 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ 455.85/67.89 X4 @ Y0)))))))))) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl73])). 455.85/67.89 thf(zip_derived_cl97, plain, 455.85/67.89 (![X2 : $i, X4 : mu, X6 : $i]: 455.85/67.89 (~ (rel_s4 @ X2 @ X6) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl84])). 455.85/67.89 thf(zip_derived_cl56, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form10' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl47, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form10' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl109, plain, 455.85/67.89 (![X2 : $i, X4 : mu, X6 : $i]: 455.85/67.89 ( ('#form10' @ X6) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))) 455.85/67.89 | ~ (rel_s4 @ X2 @ X6))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl97, zip_derived_cl56, zip_derived_cl47])). 455.85/67.89 thf(zip_derived_cl123, plain, 455.85/67.89 (![X4 : mu, X6 : $i]: 455.85/67.89 ( ('#form19' @ X4 @ X6) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl124, plain, 455.85/67.89 (![X4 : mu, X6 : $i]: 455.85/67.89 (~ (((((~) @ (rel_s4 @ X6 @ ('#sk14' @ X6 @ X4)))) | (big_p @ X4 @ 455.85/67.89 ('#sk14' @ X6 @ X4)))) 455.85/67.89 | ('#form19' @ X4 @ X6))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 455.85/67.89 thf(zip_derived_cl132, plain, 455.85/67.89 (![X4 : mu, X6 : $i]: 455.85/67.89 ( (rel_s4 @ X6 @ ('#sk14' @ X6 @ X4)) | ('#form19' @ X4 @ X6))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl124])). 455.85/67.89 thf(zip_derived_cl36, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form8' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl37, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (((exists_in_world @ ('#sk9' @ X2) @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ 455.85/67.89 ('#sk9' @ X2) @ Y0)))))))))) 455.85/67.89 | ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl36])). 455.85/67.89 thf(zip_derived_cl51, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ 455.85/67.89 ('#sk9' @ X2) @ Y0)))))) 455.85/67.89 | ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 455.85/67.89 thf(zip_derived_cl65, plain, 455.85/67.89 (![X2 : $i, X4 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ X2 @ X4))) | (big_p @ ('#sk9' @ X2) @ X4))) 455.85/67.89 | ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl51])). 455.85/67.89 thf(zip_derived_cl79, plain, 455.85/67.89 (![X2 : $i, X4 : $i]: 455.85/67.89 (~ (rel_s4 @ X2 @ X4) 455.85/67.89 | (big_p @ ('#sk9' @ X2) @ X4) 455.85/67.89 | ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl65])). 455.85/67.89 thf(zip_derived_cl638, plain, 455.85/67.89 (![X0 : mu, X1 : $i]: 455.85/67.89 ( ('#form19' @ X0 @ X1) 455.85/67.89 | ('#form8' @ X1) 455.85/67.89 | (big_p @ ('#sk9' @ X1) @ ('#sk14' @ X1 @ X0)))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl132, zip_derived_cl79])). 455.85/67.89 thf(zip_derived_cl133, plain, 455.85/67.89 (![X4 : mu, X6 : $i]: 455.85/67.89 (~ (big_p @ X4 @ ('#sk14' @ X6 @ X4)) | ('#form19' @ X4 @ X6))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl124])). 455.85/67.89 thf(zip_derived_cl39017, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( ('#form8' @ X0) 455.85/67.89 | ('#form19' @ ('#sk9' @ X0) @ X0) 455.85/67.89 | ('#form19' @ ('#sk9' @ X0) @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl638, zip_derived_cl133])). 455.85/67.89 thf(zip_derived_cl39018, plain, 455.85/67.89 (![X0 : $i]: ( ('#form19' @ ('#sk9' @ X0) @ X0) | ('#form8' @ X0))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl39017])). 455.85/67.89 thf(zip_derived_cl39, plain, 455.85/67.89 (( (rel_s4 @ '#sk4' @ '#sk6') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 455.85/67.89 thf(zip_derived_cl52, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl53, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk4' @ '#sk13'))) | 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ '#sk13') => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk13' @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl52])). 455.85/67.89 thf(zip_derived_cl66, plain, (( (rel_s4 @ '#sk4' @ '#sk13') | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 455.85/67.89 thf(zip_derived_cl68, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ '#sk13') => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk13' @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 455.85/67.89 thf(zip_derived_cl81, plain, 455.85/67.89 ((~ (((exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') => 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | (big_p @ 455.85/67.89 ('#sk9' @ '#sk13') @ Y0)))))))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 455.85/67.89 thf(zip_derived_cl93, plain, 455.85/67.89 (( (exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') | ('#form12'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 455.85/67.89 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 455.85/67.89 thf(zip_derived_cl109, plain, 455.85/67.89 (![X2 : $i, X4 : mu, X6 : $i]: 455.85/67.89 ( ('#form10' @ X6) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))) 455.85/67.89 | ~ (rel_s4 @ X2 @ X6))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl97, zip_derived_cl56, zip_derived_cl47])). 455.85/67.89 thf(zip_derived_cl123, plain, 455.85/67.89 (![X4 : mu, X6 : $i]: 455.85/67.89 ( ('#form19' @ X4 @ X6) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X6 @ Y0))) | (big_p @ X4 @ Y0)))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl125, plain, 455.85/67.89 (![X2 : $i, X4 : mu, X6 : $i]: 455.85/67.89 (~ ('#form19' @ X4 @ X6) 455.85/67.89 | ~ (rel_s4 @ X2 @ X6) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X2) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ('#form10' @ X6))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl109, zip_derived_cl123])). 455.85/67.89 thf(zip_derived_cl264, plain, 455.85/67.89 (![X0 : $i, X1 : mu]: 455.85/67.89 ( ('#form10' @ X0) 455.85/67.89 | ~ (exists_in_world @ X1 @ X0) 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ X0) 455.85/67.89 | ('#form3') 455.85/67.89 | ~ ('#form19' @ X1 @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl125])). 455.85/67.89 thf(zip_derived_cl419, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13') 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ '#sk13') 455.85/67.89 | ('#form10' @ '#sk13'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl264])). 455.85/67.89 thf(nonempty_ax, axiom, (![V:$i]: ( ?[X:mu]: ( exists_in_world @ X @ V ) ))). 455.85/67.89 thf(zip_derived_cl0, plain, 455.85/67.89 ( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((??) @ (^[Y1 : mu]: (exists_in_world @ Y1 @ Y0)))))))), 455.85/67.89 inference('cnf', [status(esa)], [nonempty_ax])). 455.85/67.89 thf(zip_derived_cl150, plain, 455.85/67.89 (![X2 : $i]: (((??) @ (^[Y0 : mu]: (exists_in_world @ Y0 @ X2))))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl0])). 455.85/67.89 thf(zip_derived_cl151, plain, 455.85/67.89 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 455.85/67.89 thf(zip_derived_cl33, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form8' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl34, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 ( (((exists_in_world @ X4 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ 455.85/67.89 X4 @ Y0)))))))))) 455.85/67.89 | ~ ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl33])). 455.85/67.89 thf(zip_derived_cl46, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 (~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | (big_p @ X4 @ Y0)))))) 455.85/67.89 | ~ ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 455.85/67.89 thf(zip_derived_cl62, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)))) | (big_p @ X4 @ 455.85/67.89 ('#sk14' @ X2 @ X4)))) 455.85/67.89 | ~ ('#form8' @ X2) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl46])). 455.85/67.89 thf(zip_derived_cl76, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 ( (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 455.85/67.89 thf(zip_derived_cl226, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 (~ ('#form8' @ X0) | (rel_s4 @ X0 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl76])). 455.85/67.89 thf(zip_derived_cl151, plain, 455.85/67.89 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 455.85/67.89 thf(zip_derived_cl195, plain, 455.85/67.89 (![X2 : mu, X4 : $i, X6 : $i]: 455.85/67.89 (~ (exists_in_world @ X2 @ X4) 455.85/67.89 | ~ (rel_s4 @ X4 @ X6) 455.85/67.89 | (exists_in_world @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 455.85/67.89 thf(zip_derived_cl196, plain, 455.85/67.89 (![X0 : $i, X1 : $i]: 455.85/67.89 ( (exists_in_world @ ('#sk20' @ X0) @ X1) | ~ (rel_s4 @ X0 @ X1))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl195])). 455.85/67.89 thf(zip_derived_cl243, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 (~ ('#form8' @ X0) 455.85/67.89 | (exists_in_world @ ('#sk20' @ X0) @ 455.85/67.89 ('#sk14' @ X0 @ ('#sk20' @ X0))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl196])). 455.85/67.89 thf(zip_derived_cl226, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 (~ ('#form8' @ X0) | (rel_s4 @ X0 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl76])). 455.85/67.89 thf(zip_derived_cl146, plain, 455.85/67.89 (![X0 : $i, X1 : $i, X2 : mu]: 455.85/67.89 (~ ('#form10' @ X1) 455.85/67.89 | ~ (rel_s4 @ X1 @ X0) 455.85/67.89 | ~ (exists_in_world @ X2 @ X0) 455.85/67.89 | (big_p @ X2 @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl121])). 455.85/67.89 thf(zip_derived_cl240, plain, 455.85/67.89 (![X0 : $i, X1 : mu]: 455.85/67.89 (~ ('#form8' @ X0) 455.85/67.89 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 455.85/67.89 | ~ (exists_in_world @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 455.85/67.89 | ~ ('#form10' @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl146])). 455.85/67.89 thf(zip_derived_cl406, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 (~ ('#form8' @ X0) 455.85/67.89 | ~ ('#form10' @ X0) 455.85/67.89 | (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 455.85/67.89 | ~ ('#form8' @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl243, zip_derived_cl240])). 455.85/67.89 thf(zip_derived_cl407, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 455.85/67.89 | ~ ('#form10' @ X0) 455.85/67.89 | ~ ('#form8' @ X0))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl406])). 455.85/67.89 thf(zip_derived_cl151, plain, 455.85/67.89 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 455.85/67.89 thf(zip_derived_cl77, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 (~ (big_p @ X4 @ ('#sk14' @ X2 @ X4)) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 455.85/67.89 thf(zip_derived_cl152, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 (~ ('#form8' @ X0) 455.85/67.89 | ~ (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl77])). 455.85/67.89 thf(zip_derived_cl408, plain, 455.85/67.89 (![X0 : $i]: (~ ('#form8' @ X0) | ~ ('#form10' @ X0))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl407, zip_derived_cl152])). 455.85/67.89 thf(zip_derived_cl40, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ '#sk6') => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk6' @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 455.85/67.89 thf(zip_derived_cl36, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form8' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl33, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form8' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl55, plain, 455.85/67.89 (( ('#form8' @ '#sk6') 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl40, zip_derived_cl36, zip_derived_cl33])). 455.85/67.89 thf(zip_derived_cl52, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl69, plain, 455.85/67.89 ((~ ('#form12') | ('#form3') | ('#form8' @ '#sk6'))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl55, zip_derived_cl52])). 455.85/67.89 thf(zip_derived_cl409, plain, 455.85/67.89 ((~ ('#form10' @ '#sk6') | ('#form3') | ~ ('#form12'))), 455.85/67.89 inference('sup+', [status(thm)], [zip_derived_cl408, zip_derived_cl69])). 455.85/67.89 thf(zip_derived_cl41, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk6' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))) 455.85/67.89 | ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 455.85/67.89 thf(zip_derived_cl56, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form10' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl47, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form10' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl58, plain, 455.85/67.89 (( ('#form10' @ '#sk6') 455.85/67.89 | ('#form3') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))), 455.85/67.89 inference('renaming', [status(thm)], 455.85/67.89 [zip_derived_cl41, zip_derived_cl56, zip_derived_cl47])). 455.85/67.89 thf(zip_derived_cl52, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk4' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y1))) | 455.85/67.89 (((!!) @ (^[Y2 : mu]: 455.85/67.89 (((exists_in_world @ Y2 @ 455.85/67.89 Y1) => 455.85/67.89 (((!!) @ (^[Y3 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ 455.85/67.89 Y1 @ Y3))) | 455.85/67.89 (big_p @ 455.85/67.89 Y2 @ Y3)))))))))))))))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((~) @ (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ ( 455.85/67.89 rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl70, plain, 455.85/67.89 ((~ ('#form12') | ('#form3') | ('#form10' @ '#sk6'))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl58, zip_derived_cl52])). 455.85/67.89 thf(zip_derived_cl415, plain, ((~ ('#form12') | ('#form3'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl70])). 455.85/67.89 thf(zip_derived_cl6347, plain, 455.85/67.89 (( ('#form10' @ '#sk13') 455.85/67.89 | ~ (rel_s4 @ '#sk4' @ '#sk13') 455.85/67.89 | ('#form3') 455.85/67.89 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl419, zip_derived_cl415])). 455.85/67.89 thf(zip_derived_cl6348, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13') 455.85/67.89 | ('#form3') 455.85/67.89 | ('#form10' @ '#sk13'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl66, zip_derived_cl6347])). 455.85/67.89 thf(zip_derived_cl415, plain, ((~ ('#form12') | ('#form3'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl70])). 455.85/67.89 thf(zip_derived_cl6383, plain, 455.85/67.89 (( ('#form10' @ '#sk13') 455.85/67.89 | ('#form3') 455.85/67.89 | ~ ('#form19' @ ('#sk9' @ '#sk13') @ '#sk13'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl6348, zip_derived_cl415])). 455.85/67.89 thf(zip_derived_cl39020, plain, 455.85/67.89 (( ('#form8' @ '#sk13') | ('#form3') | ('#form10' @ '#sk13'))), 455.85/67.89 inference('sup-', [status(thm)], 455.85/67.89 [zip_derived_cl39018, zip_derived_cl6383])). 455.85/67.89 thf(zip_derived_cl93, plain, 455.85/67.89 (( (exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') | ('#form12'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 455.85/67.89 thf(zip_derived_cl76, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 ( (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 455.85/67.89 thf(zip_derived_cl416, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ ('#form8' @ '#sk13') 455.85/67.89 | (rel_s4 @ '#sk13' @ ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl76])). 455.85/67.89 thf(zip_derived_cl94, plain, 455.85/67.89 (( (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | (big_p @ 455.85/67.89 ('#sk9' @ '#sk13') @ Y0)))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 455.85/67.89 thf(zip_derived_cl106, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ '#sk13' @ X2))) | (big_p @ ('#sk9' @ '#sk13') @ 455.85/67.89 X2))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 455.85/67.89 thf(zip_derived_cl120, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (rel_s4 @ '#sk13' @ X2) 455.85/67.89 | (big_p @ ('#sk9' @ '#sk13') @ X2) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl106])). 455.85/67.89 thf(zip_derived_cl6602, plain, 455.85/67.89 ((~ ('#form8' @ '#sk13') 455.85/67.89 | ('#form12') 455.85/67.89 | ('#form12') 455.85/67.89 | (big_p @ ('#sk9' @ '#sk13') @ 455.85/67.89 ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl416, zip_derived_cl120])). 455.85/67.89 thf(zip_derived_cl6608, plain, 455.85/67.89 (( (big_p @ ('#sk9' @ '#sk13') @ ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))) 455.85/67.89 | ('#form12') 455.85/67.89 | ~ ('#form8' @ '#sk13'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl6602])). 455.85/67.89 thf(zip_derived_cl93, plain, 455.85/67.89 (( (exists_in_world @ ('#sk9' @ '#sk13') @ '#sk13') | ('#form12'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 455.85/67.89 thf(zip_derived_cl77, plain, 455.85/67.89 (![X2 : $i, X4 : mu]: 455.85/67.89 (~ (big_p @ X4 @ ('#sk14' @ X2 @ X4)) 455.85/67.89 | ~ (exists_in_world @ X4 @ X2) 455.85/67.89 | ~ ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 455.85/67.89 thf(zip_derived_cl417, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ ('#form8' @ '#sk13') 455.85/67.89 | ~ (big_p @ ('#sk9' @ '#sk13') @ 455.85/67.89 ('#sk14' @ '#sk13' @ ('#sk9' @ '#sk13'))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl93, zip_derived_cl77])). 455.85/67.89 thf(zip_derived_cl9163, plain, ((~ ('#form8' @ '#sk13') | ('#form12'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl6608, zip_derived_cl417])). 455.85/67.89 thf(zip_derived_cl39026, plain, 455.85/67.89 (( ('#form10' @ '#sk13') | ('#form3') | ('#form12'))), 455.85/67.89 inference('sup-', [status(thm)], 455.85/67.89 [zip_derived_cl39020, zip_derived_cl9163])). 455.85/67.89 thf(zip_derived_cl67, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ '#sk13' @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl53])). 455.85/67.89 thf(zip_derived_cl80, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ '#sk13' @ ('#sk11' @ '#sk13')))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk13')) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ 455.85/67.89 ('#sk11' @ '#sk13') @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 455.85/67.89 thf(zip_derived_cl92, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ ('#sk11' @ '#sk13')) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ 455.85/67.89 Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl80])). 455.85/67.89 thf(zip_derived_cl105, plain, 455.85/67.89 ((~ (((exists_in_world @ ('#sk16' @ '#sk13') @ ('#sk11' @ '#sk13')) => 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ Y0))) | 455.85/67.89 (big_p @ ('#sk16' @ '#sk13') @ Y0)))))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl92])). 455.85/67.89 thf(zip_derived_cl119, plain, 455.85/67.89 ((~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ Y0))) | 455.85/67.89 (big_p @ ('#sk16' @ '#sk13') @ Y0)))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 455.85/67.89 thf(zip_derived_cl130, plain, 455.85/67.89 ((~ (((((~) @ (rel_s4 @ ('#sk11' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))))) | 455.85/67.89 (big_p @ ('#sk16' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 455.85/67.89 thf(zip_derived_cl137, plain, 455.85/67.89 (( (rel_s4 @ ('#sk11' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 455.85/67.89 thf(zip_derived_cl118, plain, 455.85/67.89 (( (exists_in_world @ ('#sk16' @ '#sk13') @ ('#sk11' @ '#sk13')) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 455.85/67.89 thf(zip_derived_cl195, plain, 455.85/67.89 (![X2 : mu, X4 : $i, X6 : $i]: 455.85/67.89 (~ (exists_in_world @ X2 @ X4) 455.85/67.89 | ~ (rel_s4 @ X4 @ X6) 455.85/67.89 | (exists_in_world @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl194])). 455.85/67.89 thf(zip_derived_cl543, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( ('#form12') 455.85/67.89 | (exists_in_world @ ('#sk16' @ '#sk13') @ X0) 455.85/67.89 | ~ (rel_s4 @ ('#sk11' @ '#sk13') @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl118, zip_derived_cl195])). 455.85/67.89 thf(zip_derived_cl1878, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | (exists_in_world @ ('#sk16' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl543])). 455.85/67.89 thf(zip_derived_cl1879, plain, 455.85/67.89 (( (exists_in_world @ ('#sk16' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl1878])). 455.85/67.89 thf(zip_derived_cl91, plain, 455.85/67.89 (( (rel_s4 @ '#sk13' @ ('#sk11' @ '#sk13')) | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl80])). 455.85/67.89 thf(zip_derived_cl137, plain, 455.85/67.89 (( (rel_s4 @ ('#sk11' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 455.85/67.89 thf(zip_derived_cl161, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 455.85/67.89 thf(zip_derived_cl697, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( ('#form12') 455.85/67.89 | (rel_s4 @ X0 @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ~ (rel_s4 @ X0 @ ('#sk11' @ '#sk13')))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl137, zip_derived_cl161])). 455.85/67.89 thf(zip_derived_cl7058, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | (rel_s4 @ '#sk13' @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl91, zip_derived_cl697])). 455.85/67.89 thf(zip_derived_cl7060, plain, 455.85/67.89 (( (rel_s4 @ '#sk13' @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl7058])). 455.85/67.89 thf(zip_derived_cl146, plain, 455.85/67.89 (![X0 : $i, X1 : $i, X2 : mu]: 455.85/67.89 (~ ('#form10' @ X1) 455.85/67.89 | ~ (rel_s4 @ X1 @ X0) 455.85/67.89 | ~ (exists_in_world @ X2 @ X0) 455.85/67.89 | (big_p @ X2 @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl121])). 455.85/67.89 thf(zip_derived_cl7118, plain, 455.85/67.89 (![X0 : mu]: 455.85/67.89 ( ('#form12') 455.85/67.89 | (big_p @ X0 @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ~ (exists_in_world @ X0 @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ~ ('#form10' @ '#sk13'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl7060, zip_derived_cl146])). 455.85/67.89 thf(zip_derived_cl28857, plain, 455.85/67.89 (( ('#form12') 455.85/67.89 | ~ ('#form10' @ '#sk13') 455.85/67.89 | (big_p @ ('#sk16' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl1879, zip_derived_cl7118])). 455.85/67.89 thf(zip_derived_cl28866, plain, 455.85/67.89 (( (big_p @ ('#sk16' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ~ ('#form10' @ '#sk13') 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl28857])). 455.85/67.89 thf(zip_derived_cl138, plain, 455.85/67.89 ((~ (big_p @ ('#sk16' @ '#sk13') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk13') @ ('#sk16' @ '#sk13'))) 455.85/67.89 | ('#form12'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl130])). 455.85/67.89 thf(zip_derived_cl29010, plain, (( ('#form12') | ~ ('#form10' @ '#sk13'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl28866, zip_derived_cl138])). 455.85/67.89 thf(zip_derived_cl39037, plain, (( ('#form12') | ('#form3'))), 455.85/67.89 inference('clc', [status(thm)], 455.85/67.89 [zip_derived_cl39026, zip_derived_cl29010])). 455.85/67.89 thf(zip_derived_cl415, plain, ((~ ('#form12') | ('#form3'))), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl409, zip_derived_cl70])). 455.85/67.89 thf(zip_derived_cl39038, plain, ( ('#form3')), 455.85/67.89 inference('clc', [status(thm)], [zip_derived_cl39037, zip_derived_cl415])). 455.85/67.89 thf(zip_derived_cl39377, plain, (~ ('#form17')), 455.85/67.89 inference('demod', [status(thm)], 455.85/67.89 [zip_derived_cl4225, zip_derived_cl39038])). 455.85/67.89 thf(zip_derived_cl40032, plain, (~ ('#form10' @ '#sk18')), 455.85/67.89 inference('demod', [status(thm)], 455.85/67.89 [zip_derived_cl29467, zip_derived_cl39377])). 455.85/67.89 thf(zip_derived_cl47, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form10' @ X2) 455.85/67.89 | ~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl48, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (((((~) @ (rel_s4 @ X2 @ ('#sk11' @ X2)))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ ('#sk11' @ X2)) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl47])). 455.85/67.89 thf(zip_derived_cl64, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ ('#sk11' @ X2)) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))) 455.85/67.89 | ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 455.85/67.89 thf(zip_derived_cl78, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (((exists_in_world @ ('#sk16' @ X2) @ ('#sk11' @ X2)) => 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y0))) | 455.85/67.89 (big_p @ ('#sk16' @ X2) @ Y0)))))))) 455.85/67.89 | ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl64])). 455.85/67.89 thf(zip_derived_cl90, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ Y0))) | (big_p @ 455.85/67.89 ('#sk16' @ X2) @ Y0)))))) 455.85/67.89 | ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 455.85/67.89 thf(zip_derived_cl104, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (((((~) @ (rel_s4 @ ('#sk11' @ X2) @ 455.85/67.89 ('#sk14' @ ('#sk11' @ X2) @ ('#sk16' @ X2))))) | 455.85/67.89 (big_p @ ('#sk16' @ X2) @ 455.85/67.89 ('#sk14' @ ('#sk11' @ X2) @ ('#sk16' @ X2))))) 455.85/67.89 | ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl90])). 455.85/67.89 thf(zip_derived_cl116, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( (rel_s4 @ ('#sk11' @ X2) @ 455.85/67.89 ('#sk14' @ ('#sk11' @ X2) @ ('#sk16' @ X2))) 455.85/67.89 | ('#form10' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl104])). 455.85/67.89 thf(zip_derived_cl2415, plain, 455.85/67.89 (( (exists_in_world @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl2414])). 455.85/67.89 thf(zip_derived_cl26, plain, (( (rel_s4 @ '#sk2' @ '#sk5') | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl21])). 455.85/67.89 thf(zip_derived_cl110, plain, 455.85/67.89 (( (rel_s4 @ '#sk5' @ '#sk18') | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 455.85/67.89 thf(zip_derived_cl161, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 455.85/67.89 thf(zip_derived_cl175, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( ('#form17') | (rel_s4 @ X0 @ '#sk18') | ~ (rel_s4 @ X0 @ '#sk5'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl161])). 455.85/67.89 thf(zip_derived_cl332, plain, 455.85/67.89 ((~ ('#form3') | (rel_s4 @ '#sk2' @ '#sk18') | ('#form17'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl175])). 455.85/67.89 thf(zip_derived_cl134, plain, 455.85/67.89 (( (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')) | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 455.85/67.89 thf(zip_derived_cl161, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X6) | ~ (rel_s4 @ X2 @ X4) | (rel_s4 @ X2 @ X6))), 455.85/67.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl160])). 455.85/67.89 thf(zip_derived_cl455, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 ( ('#form17') 455.85/67.89 | (rel_s4 @ X0 @ ('#sk11' @ '#sk18')) 455.85/67.89 | ~ (rel_s4 @ X0 @ '#sk18'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl161])). 455.85/67.89 thf(zip_derived_cl1365, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | ~ ('#form3') 455.85/67.89 | (rel_s4 @ '#sk2' @ ('#sk11' @ '#sk18')) 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl455])). 455.85/67.89 thf(zip_derived_cl1368, plain, 455.85/67.89 (( (rel_s4 @ '#sk2' @ ('#sk11' @ '#sk18')) | ~ ('#form3') | ('#form17'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl1365])). 455.85/67.89 thf(zip_derived_cl145, plain, (![X2 : $i]: (rel_s4 @ X2 @ X2)), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 455.85/67.89 thf(zip_derived_cl28, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ (rel_s4 @ '#sk2' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 455.85/67.89 thf(zip_derived_cl33, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 (~ ('#form8' @ X2) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X2) => 455.85/67.89 (((~) @ (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))))), 455.85/67.89 define([status(thm)])). 455.85/67.89 thf(zip_derived_cl35, plain, 455.85/67.89 (![X2 : $i]: 455.85/67.89 ( ('#form8' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X2 @ Y0))) | 455.85/67.89 (((!!) @ (^[Y1 : mu]: 455.85/67.89 (((exists_in_world @ Y1 @ Y0) => 455.85/67.89 (((!!) @ (^[Y2 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ Y0 @ 455.85/67.89 Y2))) | 455.85/67.89 (big_p @ Y1 @ Y2)))))))))))))))) 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2))), 455.85/67.89 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl33])). 455.85/67.89 thf(zip_derived_cl45, plain, 455.85/67.89 (![X2 : $i, X4 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ X2 @ X4))) | 455.85/67.89 (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X4) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))))) 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ('#form8' @ X2))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl35])). 455.85/67.89 thf(zip_derived_cl61, plain, 455.85/67.89 (![X2 : $i, X4 : $i]: 455.85/67.89 (~ (rel_s4 @ X2 @ X4) 455.85/67.89 | (((!!) @ (^[Y0 : mu]: 455.85/67.89 (((exists_in_world @ Y0 @ X4) => 455.85/67.89 (((!!) @ (^[Y1 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y1))) | 455.85/67.89 (big_p @ Y0 @ Y1))))))))))) 455.85/67.89 | ('#form8' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])). 455.85/67.89 thf(zip_derived_cl75, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu]: 455.85/67.89 ( (((exists_in_world @ X6 @ X4) => 455.85/67.89 (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))))) 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ('#form8' @ X2) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 455.85/67.89 thf(zip_derived_cl88, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu]: 455.85/67.89 (~ (exists_in_world @ X6 @ X4) 455.85/67.89 | (((!!) @ (^[Y0 : $i]: 455.85/67.89 (((((~) @ (rel_s4 @ X4 @ Y0))) | (big_p @ X6 @ Y0)))))) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4) 455.85/67.89 | ('#form8' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2))), 455.85/67.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 455.85/67.89 thf(zip_derived_cl103, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 455.85/67.89 ( (((((~) @ (rel_s4 @ X4 @ X8))) | (big_p @ X6 @ X8))) 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ('#form8' @ X2) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4) 455.85/67.89 | ~ (exists_in_world @ X6 @ X4))), 455.85/67.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 455.85/67.89 thf(zip_derived_cl115, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X8) 455.85/67.89 | (big_p @ X6 @ X8) 455.85/67.89 | ~ (exists_in_world @ X6 @ X4) 455.85/67.89 | ~ (rel_s4 @ X2 @ X4) 455.85/67.89 | ('#form8' @ X2) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ~ (rel_s4 @ '#sk2' @ X2))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 455.85/67.89 thf(zip_derived_cl250, plain, 455.85/67.89 (![X0 : $i, X1 : $i, X2 : mu]: 455.85/67.89 (~ (rel_s4 @ '#sk2' @ X1) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ('#form8' @ X1) 455.85/67.89 | ~ (rel_s4 @ X1 @ X0) 455.85/67.89 | ~ (exists_in_world @ X2 @ X0) 455.85/67.89 | (big_p @ X2 @ X0))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl145, zip_derived_cl115])). 455.85/67.89 thf(zip_derived_cl1647, plain, 455.85/67.89 (![X0 : $i, X1 : mu]: 455.85/67.89 ( ('#form17') 455.85/67.89 | ~ ('#form3') 455.85/67.89 | (big_p @ X1 @ X0) 455.85/67.89 | ~ (exists_in_world @ X1 @ X0) 455.85/67.89 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ X0) 455.85/67.89 | ('#form8' @ ('#sk11' @ '#sk18')) 455.85/67.89 | ~ ('#form3'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl1368, zip_derived_cl250])). 455.85/67.89 thf(zip_derived_cl1655, plain, 455.85/67.89 (![X0 : $i, X1 : mu]: 455.85/67.89 ( ('#form8' @ ('#sk11' @ '#sk18')) 455.85/67.89 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ X0) 455.85/67.89 | ~ (exists_in_world @ X1 @ X0) 455.85/67.89 | (big_p @ X1 @ X0) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl1647])). 455.85/67.89 thf(zip_derived_cl3819, plain, 455.85/67.89 (( ('#form17') 455.85/67.89 | ('#form17') 455.85/67.89 | ~ ('#form3') 455.85/67.89 | (big_p @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ('#form8' @ ('#sk11' @ '#sk18')))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl2415, zip_derived_cl1655])). 455.85/67.89 thf(zip_derived_cl3865, plain, 455.85/67.89 (( ('#form8' @ ('#sk11' @ '#sk18')) 455.85/67.89 | ~ (rel_s4 @ ('#sk11' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | (big_p @ ('#sk16' @ '#sk18') @ 455.85/67.89 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 455.85/67.89 | ~ ('#form3') 455.85/67.89 | ('#form17'))), 455.85/67.89 inference('simplify', [status(thm)], [zip_derived_cl3819])). 455.85/67.89 thf(zip_derived_cl134, plain, 455.85/67.89 (( (rel_s4 @ '#sk18' @ ('#sk11' @ '#sk18')) | ('#form17'))), 455.85/67.89 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl126])). 455.85/67.89 thf(zip_derived_cl151, plain, 455.85/67.89 (![X2 : $i]: (exists_in_world @ ('#sk20' @ X2) @ X2)), 455.85/67.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 455.85/67.89 thf(zip_derived_cl332, plain, 455.85/67.89 ((~ ('#form3') | (rel_s4 @ '#sk2' @ '#sk18') | ('#form17'))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl175])). 455.85/67.89 thf(zip_derived_cl226, plain, 455.85/67.89 (![X0 : $i]: 455.85/67.89 (~ ('#form8' @ X0) | (rel_s4 @ X0 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 455.85/67.89 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl76])). 455.85/67.89 thf(zip_derived_cl115, plain, 455.85/67.89 (![X2 : $i, X4 : $i, X6 : mu, X8 : $i]: 455.85/67.89 (~ (rel_s4 @ X4 @ X8) 455.85/67.89 | (big_p @ X6 @ X8) 455.85/67.89 | ~ (exists_in_world @ X6 @ X4) 456.20/67.90 | ~ (rel_s4 @ X2 @ X4) 456.20/67.90 | ('#form8' @ X2) 456.20/67.90 | ~ ('#form3') 456.20/67.90 | ~ (rel_s4 @ '#sk2' @ X2))), 456.20/67.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl103])). 456.20/67.90 thf(zip_derived_cl251, plain, 456.20/67.90 (![X0 : $i, X1 : $i, X2 : mu]: 456.20/67.90 (~ ('#form8' @ X0) 456.20/67.90 | ~ (rel_s4 @ '#sk2' @ X1) 456.20/67.90 | ~ ('#form3') 456.20/67.90 | ('#form8' @ X1) 456.20/67.90 | ~ (rel_s4 @ X1 @ X0) 456.20/67.90 | ~ (exists_in_world @ X2 @ X0) 456.20/67.90 | (big_p @ X2 @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl226, zip_derived_cl115])). 456.20/67.90 thf(zip_derived_cl894, plain, 456.20/67.90 (![X0 : $i, X1 : mu]: 456.20/67.90 ( ('#form17') 456.20/67.90 | ~ ('#form3') 456.20/67.90 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 456.20/67.90 | ~ (exists_in_world @ X1 @ X0) 456.20/67.90 | ~ (rel_s4 @ '#sk18' @ X0) 456.20/67.90 | ('#form8' @ '#sk18') 456.20/67.90 | ~ ('#form3') 456.20/67.90 | ~ ('#form8' @ X0))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl332, zip_derived_cl251])). 456.20/67.90 thf(zip_derived_cl897, plain, 456.20/67.90 (![X0 : $i, X1 : mu]: 456.20/67.90 (~ ('#form8' @ X0) 456.20/67.90 | ('#form8' @ '#sk18') 456.20/67.90 | ~ (rel_s4 @ '#sk18' @ X0) 456.20/67.90 | ~ (exists_in_world @ X1 @ X0) 456.20/67.90 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 456.20/67.90 | ~ ('#form3') 456.20/67.90 | ('#form17'))), 456.20/67.90 inference('simplify', [status(thm)], [zip_derived_cl894])). 456.20/67.90 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 456.20/67.90 thf(zip_derived_cl6492, plain, 456.20/67.90 (![X0 : $i, X1 : mu]: 456.20/67.90 (~ ('#form3') 456.20/67.90 | (big_p @ X1 @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 456.20/67.90 | ~ (exists_in_world @ X1 @ X0) 456.20/67.90 | ~ (rel_s4 @ '#sk18' @ X0) 456.20/67.90 | ('#form8' @ '#sk18') 456.20/67.90 | ~ ('#form8' @ X0))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl897, zip_derived_cl4225])). 456.20/67.90 thf(zip_derived_cl6520, plain, 456.20/67.90 (![X0 : $i]: 456.20/67.90 (~ ('#form8' @ X0) 456.20/67.90 | ('#form8' @ '#sk18') 456.20/67.90 | ~ (rel_s4 @ '#sk18' @ X0) 456.20/67.90 | (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 456.20/67.90 | ~ ('#form3'))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl6492])). 456.20/67.90 thf(zip_derived_cl110, plain, 456.20/67.90 (( (rel_s4 @ '#sk5' @ '#sk18') | ('#form17'))), 456.20/67.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 456.20/67.90 thf(zip_derived_cl207, plain, 456.20/67.90 (![X0 : $i]: 456.20/67.90 (~ ('#form3') 456.20/67.90 | (exists_in_world @ '#sk7' @ X0) 456.20/67.90 | ~ (rel_s4 @ '#sk5' @ X0))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl195])). 456.20/67.90 thf(zip_derived_cl386, plain, 456.20/67.90 (( ('#form17') | (exists_in_world @ '#sk7' @ '#sk18') | ~ ('#form3'))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl207])). 456.20/67.90 thf(zip_derived_cl76, plain, 456.20/67.90 (![X2 : $i, X4 : mu]: 456.20/67.90 ( (rel_s4 @ X2 @ ('#sk14' @ X2 @ X4)) 456.20/67.90 | ~ (exists_in_world @ X4 @ X2) 456.20/67.90 | ~ ('#form8' @ X2))), 456.20/67.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 456.20/67.90 thf(zip_derived_cl399, plain, 456.20/67.90 ((~ ('#form3') 456.20/67.90 | ('#form17') 456.20/67.90 | ~ ('#form8' @ '#sk18') 456.20/67.90 | (rel_s4 @ '#sk18' @ ('#sk14' @ '#sk18' @ '#sk7')))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl386, zip_derived_cl76])). 456.20/67.90 thf(zip_derived_cl112, plain, 456.20/67.90 (( (((!!) @ (^[Y0 : $i]: 456.20/67.90 (((((~) @ (rel_s4 @ '#sk18' @ Y0))) | (big_p @ '#sk7' @ 456.20/67.90 Y0)))))) 456.20/67.90 | ('#form17'))), 456.20/67.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl99])). 456.20/67.90 thf(zip_derived_cl127, plain, 456.20/67.90 (![X2 : $i]: 456.20/67.90 ( (((((~) @ (rel_s4 @ '#sk18' @ X2))) | (big_p @ '#sk7' @ X2))) 456.20/67.90 | ('#form17'))), 456.20/67.90 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])). 456.20/67.90 thf(zip_derived_cl136, plain, 456.20/67.90 (![X2 : $i]: 456.20/67.90 (~ (rel_s4 @ '#sk18' @ X2) | (big_p @ '#sk7' @ X2) | ('#form17'))), 456.20/67.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl127])). 456.20/67.90 thf(zip_derived_cl2576, plain, 456.20/67.90 ((~ ('#form8' @ '#sk18') 456.20/67.90 | ('#form17') 456.20/67.90 | ~ ('#form3') 456.20/67.90 | ('#form17') 456.20/67.90 | (big_p @ '#sk7' @ ('#sk14' @ '#sk18' @ '#sk7')))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl399, zip_derived_cl136])). 456.20/67.90 thf(zip_derived_cl2582, plain, 456.20/67.90 (( (big_p @ '#sk7' @ ('#sk14' @ '#sk18' @ '#sk7')) 456.20/67.90 | ~ ('#form3') 456.20/67.90 | ('#form17') 456.20/67.90 | ~ ('#form8' @ '#sk18'))), 456.20/67.90 inference('simplify', [status(thm)], [zip_derived_cl2576])). 456.20/67.90 thf(zip_derived_cl386, plain, 456.20/67.90 (( ('#form17') | (exists_in_world @ '#sk7' @ '#sk18') | ~ ('#form3'))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl110, zip_derived_cl207])). 456.20/67.90 thf(zip_derived_cl77, plain, 456.20/67.90 (![X2 : $i, X4 : mu]: 456.20/67.90 (~ (big_p @ X4 @ ('#sk14' @ X2 @ X4)) 456.20/67.90 | ~ (exists_in_world @ X4 @ X2) 456.20/67.90 | ~ ('#form8' @ X2))), 456.20/67.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl62])). 456.20/67.90 thf(zip_derived_cl400, plain, 456.20/67.90 ((~ ('#form3') 456.20/67.90 | ('#form17') 456.20/67.90 | ~ ('#form8' @ '#sk18') 456.20/67.90 | ~ (big_p @ '#sk7' @ ('#sk14' @ '#sk18' @ '#sk7')))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl386, zip_derived_cl77])). 456.20/67.90 thf(zip_derived_cl10907, plain, 456.20/67.90 ((~ ('#form8' @ '#sk18') | ('#form17') | ~ ('#form3'))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl2582, zip_derived_cl400])). 456.20/67.90 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 456.20/67.90 thf(zip_derived_cl10908, plain, ((~ ('#form3') | ~ ('#form8' @ '#sk18'))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl10907, zip_derived_cl4225])). 456.20/67.90 thf(zip_derived_cl21666, plain, 456.20/67.90 (![X0 : $i]: 456.20/67.90 (~ ('#form3') 456.20/67.90 | (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))) 456.20/67.90 | ~ (rel_s4 @ '#sk18' @ X0) 456.20/67.90 | ~ ('#form8' @ X0))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl6520, zip_derived_cl10908])). 456.20/67.90 thf(zip_derived_cl152, plain, 456.20/67.90 (![X0 : $i]: 456.20/67.90 (~ ('#form8' @ X0) 456.20/67.90 | ~ (big_p @ ('#sk20' @ X0) @ ('#sk14' @ X0 @ ('#sk20' @ X0))))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl151, zip_derived_cl77])). 456.20/67.90 thf(zip_derived_cl21667, plain, 456.20/67.90 (![X0 : $i]: 456.20/67.90 (~ ('#form8' @ X0) | ~ (rel_s4 @ '#sk18' @ X0) | ~ ('#form3'))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl21666, zip_derived_cl152])). 456.20/67.90 thf(zip_derived_cl21677, plain, 456.20/67.90 (( ('#form17') | ~ ('#form3') | ~ ('#form8' @ ('#sk11' @ '#sk18')))), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl134, zip_derived_cl21667])). 456.20/67.90 thf(zip_derived_cl4225, plain, ((~ ('#form3') | ~ ('#form17'))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl3522, zip_derived_cl129])). 456.20/67.90 thf(zip_derived_cl21736, plain, 456.20/67.90 ((~ ('#form8' @ ('#sk11' @ '#sk18')) | ~ ('#form3'))), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl21677, zip_derived_cl4225])). 456.20/67.90 thf(zip_derived_cl39038, plain, ( ('#form3')), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl39037, zip_derived_cl415])). 456.20/67.90 thf(zip_derived_cl39720, plain, (~ ('#form8' @ ('#sk11' @ '#sk18'))), 456.20/67.90 inference('demod', [status(thm)], 456.20/67.90 [zip_derived_cl21736, zip_derived_cl39038])). 456.20/67.90 thf(zip_derived_cl39038, plain, ( ('#form3')), 456.20/67.90 inference('clc', [status(thm)], [zip_derived_cl39037, zip_derived_cl415])). 456.20/67.90 thf(zip_derived_cl39377, plain, (~ ('#form17')), 456.20/67.90 inference('demod', [status(thm)], 456.20/67.90 [zip_derived_cl4225, zip_derived_cl39038])). 456.20/67.90 thf(zip_derived_cl43945, plain, 456.20/67.90 ((~ (rel_s4 @ ('#sk11' @ '#sk18') @ 456.20/67.90 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 456.20/67.90 | (big_p @ ('#sk16' @ '#sk18') @ 456.20/67.90 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))))), 456.20/67.90 inference('demod', [status(thm)], 456.20/67.90 [zip_derived_cl3865, zip_derived_cl39720, zip_derived_cl39038, 456.20/67.90 zip_derived_cl39377])). 456.20/67.90 thf(zip_derived_cl144, plain, 456.20/67.90 ((~ (big_p @ ('#sk16' @ '#sk18') @ 456.20/67.90 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18'))) 456.20/67.90 | ('#form17'))), 456.20/67.90 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl142])). 456.20/67.90 thf(zip_derived_cl39377, plain, (~ ('#form17')), 456.20/67.90 inference('demod', [status(thm)], 456.20/67.90 [zip_derived_cl4225, zip_derived_cl39038])). 456.20/67.90 thf(zip_derived_cl39894, plain, 456.20/67.90 (~ (big_p @ ('#sk16' @ '#sk18') @ 456.20/67.90 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18')))), 456.20/67.90 inference('demod', [status(thm)], 456.20/67.90 [zip_derived_cl144, zip_derived_cl39377])). 456.20/67.90 thf(zip_derived_cl43946, plain, 456.20/67.90 (~ (rel_s4 @ ('#sk11' @ '#sk18') @ 456.20/67.90 ('#sk14' @ ('#sk11' @ '#sk18') @ ('#sk16' @ '#sk18')))), 456.20/67.90 inference('clc', [status(thm)], 456.20/67.90 [zip_derived_cl43945, zip_derived_cl39894])). 456.20/67.90 thf(zip_derived_cl43948, plain, ( ('#form10' @ '#sk18')), 456.20/67.90 inference('sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl43946])). 456.20/67.90 thf(zip_derived_cl43949, plain, ($false), 456.20/67.90 inference('demod', [status(thm)], 456.20/67.90 [zip_derived_cl40032, zip_derived_cl43948])). 456.20/67.90 456.20/67.90 % SZS output end Refutation 456.20/67.90 456.20/67.90 456.20/67.90 % Terminating... 456.55/68.00 % Runner terminated. 456.55/68.01 % Zipperpin 1.5 exiting 456.55/68.02 EOF